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# Polytope of Type {2,112}

Atlas Canonical Name : {2,112}*448
if this polytope has a name.
Group : SmallGroup(448,436)
Rank : 3
Schlafli Type : {2,112}
Number of vertices, edges, etc : 2, 112, 112
Order of s0s1s2 : 112
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,112,2} of size 896
{2,112,4} of size 1792
{2,112,4} of size 1792
Vertex Figure Of :
{2,2,112} of size 896
{3,2,112} of size 1344
{4,2,112} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,56}*224
4-fold quotients : {2,28}*112
7-fold quotients : {2,16}*64
8-fold quotients : {2,14}*56
14-fold quotients : {2,8}*32
16-fold quotients : {2,7}*28
28-fold quotients : {2,4}*16
56-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,112}*896a, {2,224}*896
3-fold covers : {6,112}*1344, {2,336}*1344
4-fold covers : {4,112}*1792a, {8,112}*1792c, {8,112}*1792d, {4,224}*1792a, {4,224}*1792b, {2,448}*1792
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)( 18, 30)
( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 31, 45)( 32, 51)( 33, 50)
( 34, 49)( 35, 48)( 36, 47)( 37, 46)( 38, 52)( 39, 58)( 40, 57)( 41, 56)
( 42, 55)( 43, 54)( 44, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)
( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)
( 72, 95)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)
( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102);;
s2 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 67)
( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 81)( 18, 80)
( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 74)( 25, 73)( 26, 79)
( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31,102)( 32,101)( 33,107)( 34,106)
( 35,105)( 36,104)( 37,103)( 38,109)( 39,108)( 40,114)( 41,113)( 42,112)
( 43,111)( 44,110)( 45, 88)( 46, 87)( 47, 93)( 48, 92)( 49, 91)( 50, 90)
( 51, 89)( 52, 95)( 53, 94)( 54,100)( 55, 99)( 56, 98)( 57, 97)( 58, 96);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(114)!(1,2);
s1 := Sym(114)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)
( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 31, 45)( 32, 51)
( 33, 50)( 34, 49)( 35, 48)( 36, 47)( 37, 46)( 38, 52)( 39, 58)( 40, 57)
( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)
( 63, 90)( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)
( 71, 96)( 72, 95)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)
( 79,109)( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102);
s2 := Sym(114)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 67)( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 81)
( 18, 80)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 74)( 25, 73)
( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31,102)( 32,101)( 33,107)
( 34,106)( 35,105)( 36,104)( 37,103)( 38,109)( 39,108)( 40,114)( 41,113)
( 42,112)( 43,111)( 44,110)( 45, 88)( 46, 87)( 47, 93)( 48, 92)( 49, 91)
( 50, 90)( 51, 89)( 52, 95)( 53, 94)( 54,100)( 55, 99)( 56, 98)( 57, 97)
( 58, 96);
poly := sub<Sym(114)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope